Classification problems of multinets and conic-line arrangements

Date

2024-8

Author

Suluyer, Hasan

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In this thesis, we study the restrictions on point and line multiplicities of multinets. There is an equivalence between (3, d)-multinets and Ceva pencils of degree d curves with three completely reducible fibers for any integer d > 2. By using this relation, a fibered surface S over CP^1 is obtained by blowing up CP^2 at the base points of the pencil and each of its fibers is a strict transform of curves in the pencil which corresponds to the multinet. As the singular fibers of S may not have only nodes as singularities, a new smooth complex surface Y is obtained via the nodal reduction and the number of nodes in the special fibers of Y are calculated to get restrictions on the multinet. Also, we obtain bounds for the number of degree d conic-line curves in a pencil with |X | = d^2 by using the Euler characteristic contribution of the singular fibers of the surface S described above.

Subject Keywords

Line arrangements, Pencil of curves, Lefschetz fibration, Euler characteristic, Multinets

URI

https://hdl.handle.net/11511/110938

Collections

Graduate School of Natural and Applied Sciences, Thesis